COPENHAGEN, Denmark — The resignation of three members from the Swedish Academy awarding the Nobel Literature Prize is "deeply unfortunate and risk seriously damaging" the body's "important activities," Sweden's king said Wednesday.

The prestigious Nobel institution has been troubled by the resignation of Klas Ostergren, Kjell Espmark and Peter Englund Friday, who quit after the secretive 18-member academy voted against removing a female colleague whose husband is embroiled in sexual...